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Question
Hello, I was hoping you could help me verify this identity. I'm actually really good at the various identities and verifying them, but this problem is proving really complex for me and I just can't seem to get through it. I was hoping you could really show me step-by-step on how to get the answer for this problem.

It is:
((cos(a)-cos(b))/(sin(a)+sin(b)))+((sin(a)-sin(b))/(cos(a)+cos(b)))= 0

I created an image of it for you here, might be easier to work with visually: http://prntscr.com/2j4tlr

Thank you for your help in advance, I appreciate you taking the time to assist.

Answer
You have:

cos(a)-cos(b)      sin(a)-sin(b)
--------------- +  -------------
sin(a)+sin(b)      cos(a)+cos(b)

How about combining?  [Note abbreviations]

(ca-cb)(ca+cb) + (sa-sb)(sa+sb)
-------------------------------
[sin(a)+sin(b][cos(a)+cos(b)]

ca^2-cb^2 + sa^2-sb^2
-----------------------
[  etc  ]

ca^2 + sa^2 - sb^2 - cb^2
-------------------------
[  etc  ]

ca^2 + sa^2 - (sb^2 + cb^2)
-------------------------
[  etc  ]

Now a little trig should finish it for you.  

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